1. Field of the Invention
The present invention provides a macroscopic physical model to simulate and analyze ink ejection from a piezoelectric print head. More particularly, the model of this invention addresses the slipping contact line problem and introduces a mass-conservative finite difference implementation using the level set method so that more precise control of ink droplet size and shape can be achieved. The model may be embodied in software, hardware or combination thereof and may be implemented on a computer or other processor-controlled device.
2. Description of the Related Art
More precise control over the ink ejection process, and in particular ink droplet size, can improve the quality of the final printed product. To achieve such control, however, requires a model that accurately simulates fluid flow including droplet size and shape. Existing fluid flow models tend to impose certain conditions that lead to problems. For example, some existing fluid flow models enforce a no-slip boundary condition everywhere, which means that the triple point (the point, line or curve where three phases—two fluids and a solid—meet) does not move during simulation. While this simplifies the computations, it is unrealistic.
There are other problems that are typically encountered in trying to numerically simulate fluid flow with static or slipping contact lines. If the no-slip boundary condition for viscous fluids is enforced everywhere, the triple point will not move since the fluid velocity is zero at the wall. If one chooses to use a critical angle, which is the maximum angle allowed for the triple point to stay fixed, the conservation of mass may be violated due to no connection between the triple point movement and the fluid solver. If one chooses to solve the microscopic physics equations governing fluid flow at the immediate vicinity of the triple point, the scale of the microscopic physics will result in the need of a large amount of CPU time.